51 research outputs found
Number of Magic Squares From Parallel Tempering Monte Carlo
There are 880 magic squares of size 4 by 4, and 275,305,224 of size 5 by 5.
It seems very difficult if not impossible to count exactly the number of higher
order magic squares. We propose a method to estimate these numbers by Monte
Carlo simulating magic squares at finite temperature. One is led to perform low
temperature simulations of a system with many ground states that are separated
by energy barriers. The Parallel Tempering Monte Carlo method turns out to be
of great help here. Our estimate for the number of 6 by 6 magic squares is
0.17745(16) times 10**20.Comment: 8 pages, no figure
Improved actions, the perfect action, and scaling by perturbation theory in Wilsons renormalization group: the two dimensional -invariant non linear -model in the hierarchical approximation
We propose a method using perturbation theory in the running coupling
constant and the idea of scaling to determine improved actions for lattice
field theories combining Wilson's renormalization group with Symanzik's
improvement program . The method is based on the analysis of a single
renormalization group transformation. We test it on the hierarchical
invariant model in two dimensions.Comment: 13 pages in LaTeX, 5 uuencoded PS figures included with epsfig.sty
(including of ps-files fixed
The Hierarchical - Trajectory by Perturbation Theory in a Running Coupling and its Logarithm
We compute the hierarchical -trajectory in terms of perturbation
theory in a running coupling. In the three dimensional case we resolve a
singularity due to resonance of power counting factors in terms of logarithms
of the running coupling. Numerical data is presented and the limits of validity
explored. We also compute moving eigenvalues and eigenvectors on the trajectory
as well as their fusion rules.Comment: 24 pages, 9 pictures included, uuencoded compressed postscript fil
The renormalized -trajectory by perturbation theory in a running coupling II: the continuous renormalization group
The renormalized trajectory of massless -theory on four dimensional
Euclidean space-time is investigated as a renormalization group invariant curve
in the center manifold of the trivial fixed point, tangent to the
-interaction. We use an exact functional differential equation for its
dependence on the running -coupling. It is solved by means of
perturbation theory. The expansion is proved to be finite to all orders. The
proof includes a large momentum bound on amputated connected momentum space
Green's functions.Comment: 26 pages LaTeX2
Canonical Demon Monte Carlo Renormalization Group
We describe a new method to compute renormalized coupling constants in a
Monte Carlo renormalization group calculation. The method can be used for a
general class of models, e.g., lattice spin or gauge models. The basic idea is
to simulate a joint system of block spins and canonical demons. In contrast to
the Microcanonical Renormalization Group invented by Creutz et al. our method
does not suffer from systematical errors stemming from a simultaneous use of
two different ensembles. We present numerical results for the nonlinear
-model.Comment: LaTeX file, 7 pages, preprints CERN TH.7330/94, MS-TPI-
Running coupling expansion for the renormalized -trajectory from renormalization invariance
We formulate a renormalized running coupling expansion for the
--function and the potential of the renormalized --trajectory on
four dimensional Euclidean space-time. Renormalization invariance is used as a
first principle. No reference is made to bare quantities. The expansion is
proved to be finite to all orders of perturbation theory. The proof includes a
large momentum bound on the connected free propagator amputated vertices.Comment: 14 pages LaTeX2e, typos and references correcte
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